Sequential multiple-stage turbocharger systems are known in the art. Generally, sequential multiple-stage turbocharger systems include two or more turbochargers operating in series. In diesel internal combustion engines, such systems typically are two-stage turbocharger systems with a high pressure turbocharger stage coupled to a low pressure turbocharger stage. The high pressure turbocharger is generally smaller and has a turbine that receives exhaust gas generated by the engine. After passing through the high pressure turbocharger, the exhaust gas is received by the turbine of a low pressure turbocharger. From the low pressure turbocharger, the exhaust is received by an exhaust gas aftertreatment system, if available, and expelled into the environment.
The exhaust passing through the turbine of the low pressure turbocharger drives, e.g., rotates, the turbine, which causes a compressor to correspondingly rotate via a connecting rod coupling the turbine and compressor. Rotation of the compressor compresses intake air from the environment. After passing through the compressor of the low pressure turbocharger, the compressed air is received by the compressor of the high pressure turbocharger. The high pressure compressor is driven by the high pressure turbine via a connecting rod to further compress the air before sending the air to an intake manifold of the engine.
The rotational speeds, i.e., RPM, of the turbines must be monitored to protect the turbines from overspeed and excessive loading conditions. For example, if the speed of a turbine reaches or exceeds a predetermined upper threshold, the turbocharger system can open turbine and/or compressor bypass valves, as well as command other engine parameters, to reduce the speed of the turbine. Conventional sequential multiple-stage turbocharger systems use at least two physical turbine speed sensors, one for each of the turbines, to determine the speed of the turbines. However, compared to virtual sensors, physical sensors can be expensive and difficult to incorporate into on board diagnostic systems. Accordingly, there is a need for replacing physical speed sensors with virtual speed sensors that can accurately predict turbine speeds in multiple-stage turbocharger systems.